Newly-elected NSW senator David Leyonhjelm, who is a supporter of same-sex marriage and has traditionally opposed the plebiscite proposed by the Coalition, says he will vote in favour of it as it is the fastest way for gay marriage to become law.

After a meeting with Malcolm Turnbull on Thursday, Labor leader Bill Shorten committed to taking the idea of a public vote to his partyroom, although Labor's position has been for a parliamentary vote.

Mr Shorten has refused to say whether Labor would oppose legislation to allow for the plebiscite. Labor sources say the question to be posed to the Australian people still has to go through the Liberal partyroom, and they will decide based on the shape of the question.

Labor could also join with the Greens, the Nick Xenophon Team (whose leader Senator Xenophon has signalled his opposition to a public vote) and one other crossbench senator to block the legislation, which would give them a majority of 39.

But Mr Leyonhjelm has said he would not give Labor the extra number to take them of 39. "I wouldn't vote against the plebiscite legislation," he said, adding that, while he supported a parliamentary vote, he was not convinced the numbers in the new parliament would allow for a vote to legalise same-sex marriage. He said that, in practical terms, a plebiscite was the quickest way.